Isis Essential Standards Week 30 Essay

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ESSENTIAL STANDARDS
ASSESSMENTS
By: Isis Gill-Reid

GRAPHING TRIGONOMETRIC
FUNCTIONS
Amplitude, Period, Phase Shift, Horizontal Shift of Sine and Cosine

DEFINITION
The trigonometric functions are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other application. Amplitude is half the distance between the minimum and maximum values of the range of a periodic function with a bounded range. A graph that repeats after a fixed interval, which is a period, of the independent variable. Horizontal shift is obtained by determining the change being made to the x value. A phase shift represents the
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If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence.

Examples
Arithmetic
Sequence

Common Difference, d d add 3 to each term to arrive at the next term, or...the difference a2
- a1 is 3.

1, 4, 7, 10,
13, 16, ...
=3
15, 10, 5, 0,
-5, -10, ...

d=
-5

add -5 to each term to arrive at the next term, or...the difference a2
- a1 is -5. add-1/2 to each term to arrive at the next term, or....the difference a2 - a1 is -1/2.

REAL LIFE SITUATION
Arithmetic sequences and series are used every day by engineers, accountants, and builders.

GEOMETRIC SEQUENCES AND
SERIES
Geometric Sequence, Geometric Series

DEFINITION
If a sequence of values follows a pattern of multiplying a fixed amount times each term to arrive at the following term it is referred to as a geometric sequence. The sum of the terms of a sequence is called a series.

EXAMPLE
Geometric Sequence
Common Ratio, r r 5, 10, 20, 40, ...
=2
multiply each term

by 2 to arrive

at the next

term or...divide a2
-11, 22, -44, 88, ...

by a1 to find the common ratio, 2.

r = -2

or...divide

multiply each term by -2 to arrive at the next term
.or...divide a2 by a1 to find the common ratio, -2. multiply each term by 2/3 to arrive at the next term a2 by a1 to find the common
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